HF surgical devices of the type addressed here are basically well-known. When using electrosurgical instruments, particularly when coagulating and cutting tissue with the help of high-frequency current, the treated tissue heats up very quickly. Smoke is generated as a result of the heating, whereby the smoke may include fine particles. The smoke arising consists not only of water vapor and aerosol but may also include carcinogenic and mutagenic constituents which may be hazardous to health for the people present in the operating theatre. It is therefore necessary during an electrosurgical application to evacuate smoke immediately at the place of origin to prevent excessive contamination of the environment, in particular the operating theatre and people located therein, and to reduce the associated hazards to health. Smoke evacuation systems have been created for this reason but they frequently deliver unsatisfactory results in respect of the suction power and moreover compromise the ergonomics of the electrosurgical instruments and even sometimes obstruct the view of the operating site.